The approximate value of $$\sin \left(60^{\circ} 0^{\prime} 10^{\prime \prime}\right)$$ is (given that $$\sqrt{3}=1.732,1^{\circ}=0.0175^{\circ}$$ )

The decay rate of radio active material at any time $$t$$ is proportional to its mass at that time. The mass is 27 grams when $$t=0$$. After three hours it was found that 8 grams are left. Then the substance left after one more hour is

The derivative of $$\mathrm{f}(\tan x)$$ w.r.t. $$\mathrm{g}(\sec x)$$ at $$x=\frac{\pi}{4}$$ where $$\mathrm{f}^{\prime}(1)=2$$ and $$\mathrm{g}^{\prime}(\sqrt{2})=4$$ is

The p.m.f of random variate $$\mathrm{X}$$ is $$P(X)= \begin{cases}\frac{2 x}{\mathrm{n}(\mathrm{n}+1)}, & x=1,2,3, \ldots \ldots, \mathrm{n} \\ 0, & \text { otherwise }\end{cases}$$

Then $$\mathrm{E}(\mathrm{X})=$$